Question

Triangle LMN is reflected across a line, L = (12, –7), and L’ = (–7, 12). What is the line of reflection?

Answer 1

Option C: The line $y=x$ is the line of reflection.

Explanation:

It is given that the $\triangle LMN$ across a line, $L=(12,-7)$ and $L'=(-7,12)$

Thus, the reflection is given by $(12,-7)$ ⇒ $(-7,12)$

Now, we shall determine the line of reflection.

Option A: the x-axis

To reflect the coordinates across x-axis is given by $(x,y)$ ⇒ $(x,-y)$

Thus, the line of reflection of the coordinate L across x-axis is given by  

$(12,-7)$ ⇒ $(12,7)$

This is not the equal to the given line of reflection $(12,-7)$ ⇒ $(-7,12)$

Hence, the line of reflection is not across x-axis.

Thus, Option A is not the correct answer.

Option B : the y-axis

To reflect the coordinates across x-axis is given by $(x,y)$ ⇒ $(-x,y)$

Thus, the line of reflection of the coordinate L across y-axis is given by  

$(12,-7)$ ⇒ $(-12,-7)$

This is not the equal to the given line of reflection $(12,-7)$ ⇒ $(-7,12)$

Hence, the given line of reflection is not across y-axis.

Thus, Option B is not the correct answer.

Option C: the line $y=x$

To reflect the coordinates across $y=x$ is given by $(x,y)$ ⇒ $(y,x)$

Thus, the line of reflection of the coordinate L across the line $y=x$ is given by $(12,-7)$ ⇒ $(-7,12)$

This is equal to the given line of reflection $(12,-7)$ ⇒ $(-7,12)$

Hence, the given line of reflection is across the line $y=x$

Thus, Option C is the correct answer.

Option D : the line $y=-x$

To reflect the coordinates across $y=-x$ is given by $(x,y)$ ⇒ $(-y,-x)$

Thus, the line of reflection of the coordinate L across the line $y=-x$ is given by $(12,-7)$ ⇒ $(7,-12)$

This is not the equal to the given line of reflection $(12,-7)$ ⇒ $(-7,12)$

Hence, the given line of reflection is not across the line $y=-x$ .

Thus, Option D is not the correct answer.

Answer 2

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Step-by-step explanation: